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Cosmic parallax

Cosmic parallax. arXiv:1312.????. Syksy Räsänen University of Helsinki Department of Physics and The Helsinki Institute of Physics. Change of viewpoint. Parallax is the change in the angular position of objects when seen from different locations .

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Cosmic parallax

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  1. Cosmic parallax arXiv:1312.???? Syksy Räsänen University of Helsinki Department of Physicsand The Helsinki Institute of Physics

  2. Change of viewpoint • Parallax is the change in the angular position of objects when seen from different locations. • Can measure distance without knowing source properties. • Problem for the heliocentric system in the 1500’s. • Best current measurement by Hipparcos (1989-1993)at 100 pc. • Can be used as a cosmological test. (McCrea 1935)

  3. Motion parallax • Classic definition of parallax distance: • Naively, maximum δx=2 AU. • However, motion wrt. CMB frame is 78 AU/yr. (Kardashëv 1986) • For adiabatic perturbations, CMB rest frame is the same as the rest frame of cosmological sources.

  4. Intrinsic parallax • Assume that both sources and observers move along the same timelike curves. • The angle between a pair of sources is constant for all pairs and all observers at all times if and only if the spacetime is conformally stationary. (Hasse and Perlick 1988) • Dust matter: spacetime is FRWor stationary. • Same condition as vanishing CMB anisotropy.

  5. Parallax in general • Consider a pair of sources located in directions r1 and r2. The angle φ between them is given by • For observers moving along a timelike geodesic: intrinsic parallax motion parallax related to distance motion parallax related to image deformation (small)

  6. Parallax distance • Classic definition of parallax distance: • Suitable for a single source and spacelike separated observation points. • Real observations: relative angles, timelike separated observation points. • Modern definition: (Ellis 1971)

  7. DP and DA • ‘Parallax is angular diameter in reverse.’ • For DP, beam converges at the source, for DA it converges at the observer. (No image deformation) (Rosquist 1988) • Compare (Etherington 1933)

  8. Parallax in the FRW universe • In the FRW case there is no intrinsic parallax: • The parallax distance is(McCrea 1935) • Solving for k, we have

  9. Testing the FRW metric • If kP is not constant, the universe is not FRW. (More precisely: the optical properties of the universe are not FRW.) • This test of the DP-D relation is independent of matter content or the Einstein equation. • Test of FRW kinematics using only null geodesics. (Geometrical optics, no dynamics.) • Similar to the H-D relation (Clarkson et al 2007):

  10. Beyond FRW • Parallax can also be used to test specific models, like large voids: real-time cosmology. (Quercellini et al 2008) • Perturbations have to be taken into account: intrinsic perturbation parallax is of the same order of magnitude as the motion parallax. • Correct treatment of local motion requires non-linear treatment.

  11. Gaia • ESA satellite due to be launched on 19.12.2013 at 11.12 Finnish time. • Will measure 3 million galaxies up to z=0.75 and 500 000 quasars up to z=5. • Precision 100 μas. • Cosmological signal: δφ∼H0δx=H0vδt∼10-2 μasδt/yr. • Errors down by 1/(2N)1/2∼10-3, so feasible? (Rest frame?)

  12. Future • Cosmic parallax provides a powerful test of the FRW metric. • Will be first probed by the Gaia satellite (some parallax data out in 2016, full data in 2022). • More work needed for the cosmological analysis.

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